@EilidhMcLeodWere you able to get the DVD writer to work on your Macbook Air?
I also bought the same DVD writer, but my Macbook Air doesn't fully recognize it. I've tried it on another Macbook Air, same problem. My Windows laptop sees the DVD writer and also Windows XP via Virtual Box on my Mac sees it.
The DVD writer is visible in "system information" under "dvd burning", but it's not added to my desktop as a drive.